Philosophistry
Published in

Philosophistry

Special Relativity Explained with a Deck of Cards

Solitaire win screen

When I was taught special relativity in High School, I accepted the theory as true, even though it never sat right with me. A few months ago, I decided to read and watch every special relativity lesson I could find until I was blue in the face. Finally, it all made sense when the Solitaire win screen popped into my head, making the theory as easy to explain as a deck of cards.

Thanks to Einstein’s theory of special relativity, we now know that all sorts of spooky things happen in our universe. For example, if your dad entered a spaceship and traveled at half the speed of light, away from Earth, and then returned, he would be the same age as you.[1] Wait, what?

According to special relativity, time slows down noticeably if you move really fast. And this isn’t just theoretical. GPS satellites that move away or towards each other will have their clocks out of sync, enough to cause navigation errors. Or if you were to send a watch on an airplane that flies around the world, when it returns, it would be slightly behind the watch on your arm.

Taken to its logical extreme, a form of time travel is possible in our universe. Even though the film Interstellar is science-fiction, the scene with a 35-year-old Joseph Cooper (played by Matthew McConaughey) returning to Earth to meet her 100-year-old daughter Murphy Cooper, is grounded in science-reality:

Thinking Four-Dimensionally

To understand how this works, we have to change our understanding of time. We need to think in four dimensions. Even though we’re limited by the two dimensions of this page, we can illustrate four-dimensional timelines with a deck of cards. This is a timeline of you standing still:

This is a timeline of you walking:

For the most part, because the relative speeds of objects are much smaller than the speed of light, most timelines end at the same spot. The similar timelines are apparent when you show the decks stacked side-by-side:

If you stack two decks next to each other, and shift one slightly to the right, their heights should be the same. This matches our day-to-day experience. For the most part, when a friend of yours walks away from you and comes back, your watches will show the same time. When you and your classmates have a reunion, you will all have (hopefully) aged at the same rate.

But let’s say you had a superpower, like Flash Gordon, where you could run at half the speed of light. The deck of cards would fan out, like on a card table. Now compare the heights:

The speeding version of you and the standing version of you no longer arrive at the same moment in the same amount of time.

The physics behind this

Einstein understood that space and time are a single continuum. When you move “forward” one second, you are actually moving forward in time 186,282 miles (seven-and-a-half Earth circumferences), which is the distance light travels in one second. That’s right, time can be measured in miles! And every particle of our body is zipping forward at the speed of light.[2]

As a result, when we move, what was once the speed of light going forward in time gets diverted to other dimensions. Otherwise, your speed through spacetime would now be faster than the speed of light.

Einstein figured this all out by asserting the simple postulate, that the speed of light is constant, and then taking the math to its logical conclusion. The result is a universe that behaves a lot differently than our day-to-day experience. In our daily lives, everybody is synchronized to one clock. But out in space, with celestial objects moving at noticeable fractions of the speed of light, relative to each other, every object keeps its own time.

[1] The Twin paradox is used here just to make it concrete in the reader’s mind that things age differently depending on how fast they move. We could change the thought experiment by removing the return trip of your father, but then we’d have to explain observational frames, which is beyond the scope of this article.

[2] 4-velocities are normalized to the speed of light.

--

--

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
Philip Dhingra

Philip Dhingra

Author of Dear Hannah, a cautionary tale about self-improvement. Learn more: philipkd.com